Question: 

How can I see the consumed energy of a time-period in Energy Analyze ? 

Answer: 

Open the *fca-file containing logging measurements in Fluke Energy Analyze. 
Then go to the tab Energy Study and select there Demand : 

In the menu on the right you need to set a few items to get the view you are looking for. 
Select in the tab Ep [Wh]  - Total and cumulative. 
On the Time range select Individual and Set Time Range : 

At the bottom of the graph a Demand Time range Table selection is added as soon as you tick 'Set Time Range' at time range.
You might need to pull this up a little in order for the number to be visible together with the graph.

By moving the cursors you can see the consumed power between the cursors in the table below the graph.